Using tesselations to design patchwork quilt patterns

A tesselation is a collection of tiled shapes which fill a space with no gaps and no overlaps. This concept translates beautifully to patchwork, where the fabric blocks which make up the pattern must fit together to allow the finished quilt to lie flat. Today we’ll look at how you can use paper, scissors, and simple tesselations, to design a large variety of patchwork patterns. We’ll also look at how to make an irregular patch.

The simplest kind of tesselation is one of the three regular tessellations – made up of squares, equilateral triangles, or hexagons (which are themselves made up of tessellated equilateral triangles). Simple as these may seem, when we add colour (or different fabrics), there are a huge number of patterns that can be made up using only one of these three regular shapes. Here are four patterns made up of just equilateral triangles in three colours – you can see the scope for variety.

These three regular shapes can also be combined, if their sides are the same length, to make a number of other tilings. Here are four different patterns made up from a simple arrangement of squares and triangles.

Many other shapes, regular and irregular, will tesselate if combined in the right way – all four-sided shapes will tile quite happily, for example, and even shapes that will not tile regularly, such as regular pentagons, will tessellate in combination with other shapes. A quick image search for ‘tessellations’ will give you a snapshot of the many beautiful designs that can be made up by simple repeating geometric shapes.

Today, let’s have a play around with just two shapes, a square and an equilateral triangle.

You’ll need:

• Paper and pencil
• ruler
• protractor
• stiff card
• origami paper or other coloured paper
• scissors and glue

First we’ll draft our two shapes – making the lsides of both shapes the same length. An equilateral triangle, you’ll remember, has three angles of 60°. Trace the shapes onto card and cut them out.

You now have two stencils which you can use to cut out a stack of coloured paper squares and triangles – if you already have your fabrics in mind, use as many different colours as you have fabrics.

You can see from the image below how I began by finding a way of fitting the shapes together that I found pleasing. I then changed the colours around until I liked the result, and pasted them down so that I could easily remember my design.

All my shapes fit together to make larger shapes – a rectangle, a hexagon, and a large triangle made up of three small ones. I was able to use my small shape stencils to make some larger stencils for the actual quilt pieces. Shapes can also be cut in half, as well as combined, adding two different right-angled triangles to the mix.

Finally I traced the stencils onto the fabric, and made up my patchwork. You may remember an earlier post on how to hand-piece patchwork.

As well as tiling regular shapes, you can design irregular shapes which will tessellate. Here’s one of the easiest methods to do this.

You’ll need:

• Paper
• Pencil
• scissors
• tape

Begin with a small piece of paper – square or rectangular is fine. Draw an irregular line from top to bottom edge, and a second irregular line from side to side. Cut out along these lines. Lay out the paper as it was before cutting, and then swap pairs of corners diagonally, so that the square corners are now in the centre. Tape together, and you now have your stencil. The shape, though quite random, will tessellate as you can see (allowing for some irregularities in cutting).

Starting with just a few paper shapes, you can create a boundless number of lovely and unique quilt designs. Have fun!

You may also like:

1. How to hand-piece patchwork – simple coaster
2. How to design an amigurumi
3. How to design Amigurumi Part 4 – Octopus